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Fluctuation theorems and the generalized Gibbs ensemble in integrable systems.

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We derived new quantum fluctuation relations for many-body systems. These relations reveal quantum criticality signatures in work and entropy statistics for the quantum Ising model.

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Area of Science:

  • Quantum mechanics
  • Statistical mechanics
  • Condensed matter physics

Background:

  • Generalized Gibbs ensemble describes isolated quantum systems.
  • Non-equilibrium quantum dynamics are crucial for understanding thermalization.
  • Fluctuation relations connect microscopic work to macroscopic thermodynamics.

Purpose of the Study:

  • Derive generalized fluctuation relations for quantum systems.
  • Investigate these relations in isolated integrable systems.
  • Explore signatures of quantum criticality in non-equilibrium processes.

Main Methods:

  • Formulate generalized fluctuation relations.
  • Apply methods to isolated integrable many-body quantum systems.
  • Analyze the one-dimensional quantum Ising model under a transverse field quench.

Main Results:

  • Generalized Tasaki-Crooks and Jarzynski relations derived.
  • Work and irreversible entropy statistics exhibit quantum criticality.
  • Signatures of quantum criticality observed in the quantum Ising model.

Conclusions:

  • Fluctuation relations provide insights into non-equilibrium quantum dynamics.
  • Quantum criticality influences thermodynamic quantities in driven quantum systems.
  • The study offers a framework for understanding thermalization in quantum critical regimes.